The minimal social situation, which arises in living systems and subsystems at the level of the group, is a two-person game of incomplete information in which the players are ignorant of their interdependence. The win-stay, lose-change principle, based on the law of effect, explains how they nonetheless learn to cooperate when the game is repeated many times. In this paper the minimal social situation is generalized to groups arbitrary size with the original two-person game representing a special case. Some theorems are derived from the assumption that the players follow the win-stay, lose-change principle, and the circumstances that result in joint cooperation are formally characterized. Whether or not an iterated multiperson minimal social situation results joint cooperation under the win-stay, lose-change principle is shown to depend on the configuration of initial choices and the number of times that the group size is evenly divisible by two. Finally, some implications for experimental research are outlined.